and...

it WAS David Kelly, but apparently at some point in the post Kelsey Grammer era, but is not now...

"Voice of Geico Gecko Updated
Kelsey Grammar, of Frasier fame, provided the voice for the first ad. From there on the British accent was provided by Dave Kelly. For the most recent Geico Gecko campaign the accent is Cockney. There's some debate about who the actor now is. I believe it would be impossible to pick the actor from the accent as a 'voice' can be developed to suit the demands."